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Iowa State University
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Re+'*ec+-e e*e* a&d D**e+a+'&*
1949
A piezometer method of measuring soilpermeability and application of permeability data to
a drainage problem James Nicholas Luthin Iowa State College
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A PIEZOMETER METHOD OP MEASURIIG SOIL
PKRMEABILITY
AID
APPLIGATIOI
OF PERMEABILITY
DATA
TO A DRAIIAGfi
PROBLEM
by
James Micholas LutMa
A fliesis Submitted to the
Graduate Paeiilty for the
Degree of
DOCTOR OF
PHILOSOPHY
Ma^or Subject; Soils
Approved;
Head of Major Department
Dean
of 'Graduate Ooliege
Iowa State
College
1949
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S59f
L317P
-ii-
fABLl OF COITEHTS
Page
I.
IlfRODUCTIOI
1
II. RE?IEf
OF
LITSRAfURE 4
A. Darcy's
Law
4
B. Equation of Flow 7
0. PerBieability Units 9
D. Methods of Measurement 10
1. Laboratory metliods 11
a. The
disturbed
sample 11
b.
The
undisturbed sample 11
2.
Indirect methods . 12
3. Field methods
12
a. Unlined wells 12
b.
Lined wells 13
e. tracers 14
S.
Factors Affecting Soil Permeability 15
1.
Entrapped
air
15
2. Microorganisms 17
3. Salts
20
4.
Temperature
20
F. Solution of Flow
Problems
21
1.
Analytical methods 21
a. Bapuit-Forchheimer theory 21
b.
Kirkhaai-Gardnex
approach .
25
2. Graphical
methods
of
Dachler,
Caaagrande,
and Forehheia er
26
3.
The
hodograph
27
4. Membrane analogue 28
5. llectrical analogue 29
lumerical methods
31
T
^0
40
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-iii-
Page
III.
THl PROBLIM
36
A. Piezometer
Method for Measuring Soil
PeriaeaMlity
,
...
36
1. Field
procedure
36
2. Field tests . 40
3. Laboratory
procedure
..... 45
4. Results
of
field tests
..........
0
5.
Laboratory
results 68
B.
Application of
Permeability
Data
to
a Drainage
Problea 73
1. Procedure 74
a.
Draimage
of
soil
with
uniform
p e r r a e a b i l l t y
.............
7 7
b, Dralmge of soil with non-uniforw
permeability
84
IV. GONGLUSIOIS AID SUMMAET 96
¥. LITSIATURI
OlfED
97
¥1.
ACIIOfLED^ffilT .103
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xao.
1
2
3
4
5
6
7
8
9
10
11
13
Page
5
51
52
53
54
56
57
59
61
62
63
94
-i¥-
LIST OF TABLES
Relation
of
Preesmre
to
Flow Through Glay-
SeelhMai
( 0).
Field Test Data
Field Tftst Data
Field Test D®.ta
Field Test Bata
Field Test Data
Field Test Data
Field Test
Data
Field Test Data
Field Test Data
Field
Test Data
Results
of
luraerieal
Analysis
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-V-
LIST
OF FiaURlS
Fig. Page
1
Illustrating
Darcy*e
Law. Gardner (38). 6
8 Changes
in
Peraieability of
Soils During
Long
Submergence. Allison (l), 18
3
PermeaMlity-fime
Curves
for Hanford
Loa®
Under
Prolonged
Submergence. Allison
(l).
18
4 Dupuit-Forchlieimer
Theory
of Soil Drainage. 24
5
Points
on let 34
6 Relaxation
Pattern.
34
7
Piezometer Method of Measurement of
Permeability. 37
8 Installing the
Piezometer.
37
9 Flushing out the
Piezometer.
39
10 Applying Suction to the Piezometer.
Upper
Stopper
is for
a 2-lnch Piezometer.
39
11 Measuring Water Elevation with Reel-Type Electric
Probe
44
12 Removing a
l-inch Piezometer with
Veihmeyer
Soil
Tube Jack.
44
13 Cirmiit for Location
of
Equipotential Surfaces. 47
frevert (27).
14
Circuit
for
Determination
of A-function* Frevert
27) 47
15 Plot of Field Data to Show Linear Relationship
Between In(d-y) and Time
t.
48
16 Variatioa of A-funotion
with
Diamete r of Cavity for
a
4-inch
Long
Cavity
(For
Values
of s and
d
See
Text). 69
17 Variation of
A-function
with Length
of
Cavity for
a 1-inch Diameter
Cavity (For
Values of s
and d
See Text).
69
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-•ri-
Fig. Page
18
fariation of
A-fuactioii ?dth. s,
for a
Cavity 4-
iaehes leag and l-iach in Maaeter. 71
19
Iqiiipotential
Surfaces
for
a Piezometer
Cavity.
71
20
Sxample of
Mtbaiaim Proeedure, 75
21 Iquipoteatial Plots for Gase
of
iDralnag© of
Uniform Soil.
S©« Text
for Details.
80
Point l€ar a Gurved Boundary.
81
23
Point on an Interface.- 86
24
Point a t Upper Oorner. See Text.
89
25
Point
a t
Lower
Oorn®r,
S@e
Text.
89
26 Iquipottntial
Plot
for Drainage of a Two-layered
Soil. 91
27 Icpipotential
Plot
for Drainage
of
a Two-layered
Soil. 93
28
fiquipotential Garves for Drainage of a Two-layered
Soil 93
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I.
IITROOTGTIOir
It has long toe®n recognized that soil permeability is an
iBEportant
factor in land management, soil conservation and
land
drainage.
Muoh work
has been d x j n e on methods
of
measuring
soil
permeability and various sehemes have been devised to apply the
information to
the
design of
drainage
systems, dams and other
engineering structures.
In general, the
measurement
of soil permeability has con
sisted of taking
a sample of
soil
from the field
into the labo
ratory in either
a disturbed
or an undisturbed state, passing
water
through the
sample,
and determining
it s
permeability by
use of suitable equations. Such methods of permeability meas
urement have been unsatisfactory for many reasons.
Recently
several
faethods
of
determining
soil
permeability
in
the
field have been proposed.
In
1936 Hooghoudt
augered
out
a hole in the soil bel ow the water table and observed the
rate
of rise of water in the
hole.
By means of
approxiLiate
formu
las
he
was
able to
calculate
the soil
permeability.
Kirkham
and Van Bavel pointed out certain defects in
Hooghoudt's
formu
la
and derived
a
more exact equation
based
on
a solution
of
Laplace's equation.
They
tried
out
the
method
\?ith success
on
several Iowa soils.
In 1945, Kirkham proposed a field method of measuring
soil
permeability x ' y h i c h
consisted
of
driving
pipes
into the
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-2-
soil below a water
table and
meaiuring the outflow
of
water
frotB
the
pipe® into
the
soil. This
proposed method was tried
out
by
Fre^ert
and
Kirfchaa,
They
found that it
was
necessary
to
remote the soil
from
the interior of
the
pipe and they also
noted
that
a
lauoh laore
aecurate measure of the permeability
was
obtained by permitting the water
to
flow into the
pipe
from the
soil rather than using
the outward flow from the pipe into the
soil. Because driving the pipes into the soil
compresaed
the
soil,
they
had to
use pipes of large diaaeter (8 inches). The
depths
to
which the
soil
permeability could be
measured
were
lifflited to
36 inches
because of the equipment used, and special
tools were needed to remove
the
pipes from the
ground.
the preceding fiel d methods have in common certain ad
vantages over any laboratory methods which have been proposed.
First, the
soil permeability is measured in
situ; second, soil
water is its e lf
used
for the measurement; and third,
root holes,
worm
holes,
and rocks have a negligible effect on
the deter
mination.
There are, however, certain limitations
to these field
aethods. Both
of them
are
limited to shallow depths below
the
soil surface and the auger hole method, as it gives a sort of
average permeability over
the length
of the auger
hole, will
not
Indicate
the
permeability
of
specific layers
or
horizons.
To overcome the limitations of the above methods, a new
procedure, utilizing
pipes of small
diameter (piezometers).
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- • o « »
has been developed.
T i i e
method consists basically in measuring
the
ratt
of
flow into a canity at the base of an emptied pie-
^offleter.
Advantages
of
the
method
are
(l)
the
permeability can
be measured to great depths, (2) the permeability of any layer
in
the soil
can be measured, (3)
the
method is quick, acciirate
and
simple, fhe deirelop»ent
of
this method, \i^ich includes
use of a three-dimensloiial electric analogue of the groundwater
problem., constitutes two parts of t&ls thesis.
Kirkhaa
has
solTed the problem of
steady-state flow into
tile drains in
a uniform
soil but
there is
no general solution
that
will handle
all
of the complex Tarlations found in natural
soil. Similar types
of
problems are encountered
in
the fields
of heat flow,
electricity,
and hydrodynamics and various in
vestigators have developed
numerical methods of obtaining ap
proximate solutions
to
any desired degree of accuracy.
Because
of the simila rity
of
these
types
of
problems,
it
is evident
that
numerical
method®
qbm
also
be
applied to problems of
land
drainage. The development and application of suitable numerical
methods to land drainage constitute a third part of this thesis.
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-4-
II. REVIEl OF IiITSRATURE
A f f l o r e
thorough review
of
the literature
on
soil
permea-
bllitir can he found in
Freveart's
(27) thesis. However this
subject will
be
covered here
in
brief.
A. Darcy's Law
The
rBDvemeat
of fluids
through
porous
media has
long been
of great practical importance to agriculturists concerned with
irrigation and drainage and to engineers interes ted in the flow
of fluids
into
wells
and
through filter beds. Since most porous
media
can be regarded
as
a
macroscopic
collection
of
more
or
less discontimioua capillary tubes,
the
first
experimental
studies which
can
b©
regarded as forming t he basis of our pres-
ent-day
knowledge
of
water
flow
through soils
were
performed
by Hagen
(32) in
1839 and
by
Poiseuille
(53) in 1846.
These
investigators
studied
the
flow of fl uids through capillary
tubes
and from
their observationa concluded that the
rate
of
flow
is
proportional 1 ; o
the hydraulic gradient.
In 1846 a French hydraulic eiigineer,
Darcy,
used experi
mental
methods
to study the flow of water thro\;^h sand filters.
His classic experiments led to the result - now
referred
to as
Darcy*9
law
- hat the
rate
of flow of wate r through the
fil
ter bed
was
directly proportional to the
area of
the sand and
to the diffe rence
of the
fluid
heads
at
the inlet
and
outlet
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—5—
faces
of
t h t e
bed,
and In-^erssly proportional to
the
thickness
of the hed. (See fig. 1.) Expressed mathematically, Darcy*8
law
becomes
Q K I (1)
where
Q =
discharge "velocity
K = coeffioient
of
periseatoility
A
s
cross
sectional area of bed
L
=
length of bed
h
«
difference in head between outle t and inlet faces.
The •B'alidity of
Darcy*s
law has bee n confirmed
by
many
experimenters,
aost
of
ôm
used sand separates
in their t est s.
Since OUT main interest is
the
application
of Darcy*3
law to
the
moveraent of
wate r through
soils
we
may
consider SeelhetM
(60) to be the first in-s'estigator
to
use
soil in
a check of
Darcy's
law.
The
data
(in
part)
-hich
SeeHieim
obtained
is
Included in table
1.
fable
1
Relation of
Pressure to Flow Through
Clay
- Seelheim (60)
Pressure
list
SjISas.
Me^
150 G f f l . 60 12 c 0.59
cc
100 cm. 60 13 c 0.39 cc
fhese results, though limited, ooafirm the
application
of
Darey*s l a t t to fluid flow through clay.
Teraa^hi (66) in
1925 showed
that Darcy*s law can be ap
plied to the flow of water through clay and concluded that it
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y=k(h,-h;) h,-h.
t-v=kV$]
V
Fig.
1.
Illustrating Darcy*s
Law.
Gardner (38)
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7̂-
may be
safely
applied to grouad-irater flow.
Kiag (40) ia a review of earl ier work pointe d out that the
relatioaship between
the
quantity
of
water
transmitted
throvigh
the soil with increasing pressure (or hydraulic gradient) did
not always follow a straight line.
In
many cases the quantity
of
water
discharged
did
not
increase as much as
the
pressiire.
This
was
especially
true
for
very porous substances
such as
gravel
or
where the hydraulic gradient was so large as
to
cause high velocities of the water moving t hrough the material.
This
departure from
Darcy's law
has
been satisfactorily
explained on
the
basis of
Reynolds*(55) work
with
capillary
tubes. At low velocities the movement of the
water
is laminar
(in straight lines) and the only force opposing its motion is
the
resistance
of the
walls of
the
capillary tubes
(or
soil
parti'cles).
Ihen its velocity
increases
over a certain value,
then the flow
becoaies
turbulent and part of
the
energy of the
moving
liquid is
dissipated in eddy losses. The flow is
re
duced because of these energy losses in
eddy
currents
(see
Muskat
51,
p.
56). The
velocities
normally encoimtered in
the aoveiaent of water through soils are well within
the range
of the validity of Darcy's law
and so we may safe ly apply it
in our soils work.
B. Equation of Flow
Darcy's
law
as originall y formulate d applie d to flow in
/
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8̂-
one direction and nay
be
rewritten
ia differential
form, substi
tuting Telooity v for discharge Q, and taking A »
1
as
V
=
K
(2)
oh
where is the hydraulic gradient in
the
direction
h.
Slichter (63) was the first to show how Darey's law
can
be ap
plied to flow in any direction by rewriting eq, (3) in the form
where
4̂ hydraulic gradient
la
any
direction s.
In case no
o s
external
attractive forces
are
acting and
K^, Ky,
K^, represent
the soil peraeability in the x,
y,
z directions then
the
equa
tion
of continuity
as deriTed by Slichter
(63) ia
(3)
which is
a osathematical statement that the
liquid
is
inco/a-
preasible
- hat is, a
given
taass
of
the liquid does
not chaise
its volume during the given motion.
If K j j
s
y - g (ie, the soil is hostogenecaas) then eq. (3)
becomes
^ ill = 0
which is Laplace's equation, an equat ion that occurs frequently
in mathematical
physios.
The
function
is
called
a potential
function.
Thus
the
solution
of
any
ground
water
problem depends
on
a
solution
of Laplace's equation as
pointed
out
by Slichter
(63).
To
Slichter also
goes credit
for
showing that the motion
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^9-
©f ground water is analogous to the flow
of
electricity,
the
fl©w
of
heat, or to a problem
In the
steady
motion
of a perfect
fluid. Slichter noted that
the gravity
factor should be
included
in the equations of motion
and
much of the present day work on
the theory of ground-water moveffient is based on the relationships
discoirered
toy
him.
C. Permeability Onita
Although
soil
permeability has
been
under intensive investi
gation for almost 100 years, there is still no generally accepted
method of e xpres si ng the permeatoillty factor
or
coefficient (K in
eq. 1). Richards (56) suggested that k
in
the equation
V s ki (5)
where
v « quantity
of
water flowing
per
unit
time per
unit area
i
a s hydraulic
grMient
be used. This is
the
Daroy
coefficient
and has
the convenient
dimensions of velocity (e.g.
c®
per sec). (The effect of vis
cosity
is
included
in
eq. (S)
as a
dimensionless ratio.)
Veloc
ity of flow
is
in
common
usage in engineering and hydrologic
work and
posse sse s certain
advantage over other methods of
ex
pression.
BodraanC?)
has
suggested
a
unit
of
permeability
having
the
dimension of time
according to the
following equation.
^ • 8 =
f-i-l/h
where
Pg
«
permeability
coefficient
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-10-
g/h = hydraulic gradient
Q/t
= discharge velocity
A
« orosB sectional
area
1 « •
length
of column
Wyckoff, Botsetj Muskat and leed (73) have introduced th«
visoosity
of
the fluid into
Darcy's equation, thus
giving K,
tie
dimension of an area.
This coefficie nt waa called the "darcy*
and
was
defined as the voluiae of fluid of one centipoise vis
oosity pas sing throu^ a
one square om. cross section in
one
second under the action of a pressure gradient of
one
atmos
phere per
o a i .
Richards
(57)
later presented
a
new unit
called
the
"dar**,
which had
the
dimension of time and was numerically equal
to
the
mass
of the liquid crossing unit area in
unit
time per
unit pressure gradient per
centipoise
viscosity* This
uait
had
the a dvantage that it
was
independent
of the
system
of
measurements
used (metric or English) and was also adaptable
to
a wide range in permeabilities.
Edlefsen (20,
p.
431* 432) pointed out
that
"In some
studies, it
is
probably preferable
to use one form of
the
permeability-coefficient, while in other
studies, it
might
be more convenient
to
use a
diffe rent form."
D.
Methods of Meas urement
lo
attempt
will be made
here to
review
al l
of the
various
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methods
of
measuring permeability,
sinoe there
are almost
as
many methods
in
use
as t here
are investigators,
tout
rather some
of
the
general fe atures of
each method will
be
described.
1.
Laboratory methods
a.
The disturbed sample.
In the use of disturbed soil samples the soil ia collected
in
the
field and is packed into permeameter
tubes in the labo
ratory. Mo
special attempt is laade
to preserve the
natural
structure of the
soil
when filling the
permeameter.
This
method has
met
with success in
its
application on the struc
tureless
soils
of Western United States
in studies
of
the
effects of various treatments on soil permeability. The
permeability values obtained are not necessarily related to
the permeability
of
the soil in th^ field but serve
to
indi
cate
the relative effects that various soil treatments might
have in the field. Fireman (22, p.
337)
discussed this method
in detail and
stated
that,
In
many cas es permeability values obtained
In
the laboratory may not even
sp
proximate the
percolation rates....reliminary tests
indicate that, regardless of the correlation
between laboratory
and field
percolation
rates,
the relative
change
in permeability obtained in
the
laboratory
as a
result of
any given
treat
ment
is
closely
correla te d with the relative
change
in percolation rate obtained
in
the
field
as
a result of a
similar
treatment.
b. The undist\irbed
sample.
¥arious
investigators
have devised methods of
obtaining
so-called
undisturbed soil
samples. In general these methods
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h we consisted of inserting a metal cylinder into
the
soil and
removing the
cylinier
filled i t f i t h
soil. The soil-filled
cylin
der
is
then
taken
into the
laboratory
where
permeability meas-
mrements
are made. Large
errors enter into the
determination
because of the presence of
root holes
and rock
in a
sample that
is
necessarily
small and
the
tremendous variation between repli
cates makes it
impractical
to
apply the
results
in the
field.
2. Indirect
methods
Many soil
properties
such
as
hygroscopicity
(59),
pore
sise distribution
(3,
4, 5,
49, 52),
point
of inflection
on
a
pF
curve (3), size and shape of the soil grains
(63),
per
centage
of
elutriable
particles of certain
sizes (59), have
been used
in
an effort to
find some
soil property
that can be
correlated with soil permeability.
In spite of the great amount
of
work
done no generally satisfactory
method
has been
foxuid
that can be applied to soils over a wide region. Firensan (23,
p. 340) in a discussion
of
indirect methods
of
making
permeability
measurements concluded that,
Kiese
methods have not
been of
particular
value
except in special cases such as
the evaluation
of probable
permeability
to air. . . .,
nor
do
they usually
involve a saving in
effort
or expense.
3. Field methods
a. Unllned
wells.
fenzel
(71)
in
a
review of the literature on
methods of
permeability measurements classified
the
methods of
measuring
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-13-
permeaMllty
froa unlined wells as
those imrolvliig observations
oa the drawdown of the well
and those
involving the rate of re^
covery of the water table.
?ariome
equations have
been
devel
oped for calculation of the permeability from the above meas
urements.
A
basic
assumption of
the
derivation is that the
Gone of depression
around
the discharging well has reached
equilibrium (steady-state flow of water). Jacob
(39)
has de
veloped a foriTOla based
on
a
nonequilibriiiffl state.
In
the
field of
soils Diserens
(18)
and Kozcny (47) have
proposed digging an auger hole into the soil, and observing the
rate
of
rise
of the water in
the
hole.
Hooghoudt (38)
developed
formulas for
calculating
the
soil permeability
from the
observed
rate
of rise
of the water in
the
hole
but his
equations
are
not
based on solutions of Laplace*s equation and their validity has
been questioned by Kirkham (45). Kirlcham and Van Bavel (45) and
Tan
Bavel
and
Klrkham
(68)
have
developed
©ore exact
formulas
based on solutions
of
Laplace*s equat ion and have applied the
method
to several Iowa soils.
b. Lined wells.
The
lined
well
method consists of inserting
a tube,
pipe,
or cylinder into the soil and observing
the
rate of flow of
wate r into or out
of
the
pipe. This method
has been widely
used (26) in
a
study
of
the relative
rates
of
infiltration of
water into different soils. Suitable
equations
for calculating
the soil perioeability from these observations
were lacking
un
til lirkham (41)
in
1945 solved the problem for a steady-state
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14-
oondition. The method
of permeaMllty meaeureraent
developed
in this paper makes use of the formulas given
by
Kirkham and
follows somewhat the
methods
proposed
by him.
larlier in 1932
Kozmy
(46) propose d a simil ar method of
driving tubes 10 O f f l in diameter below the water table and ob
serving the rate of fall of wster in the pipe after the soil had
been removed from the interior of the pipe. The formulas which
Kozmy
developed were based
on
several approximations
and
Kirkhaffi (41) has questioned their validity,
e.
Tracers.
Tracers
have
been
effectively used to
measure
the velocity
of ground-water movement and
the
results have been summarized
by
Tolman (67) and
fensel
(71).
Tracers that have been used
include s a l t solutions of 11401 and laOlt and dyes such as
flourescein.
The
movement
of
the
salt
solutions
has
been
followed
by
observing the change
in
electrical conductivity of the ground
water. Wenzal
(71)
in a discussion of the use of
s a l t
solu
tions
a s
tracers pointed out that salt water is heavier than
the
ground-water
and l a a y
flow downward so as to
miss
the
point
at which the sample is taken,
Tolman
(67)
in a
discussion
of
the use of
dyes aa tracers
stated that
they
may
be more accurate
than sa lt
solutions
but
their us©
is
Halted due
to their interaction with the
organic
matter of the soil.
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•15-
S.
Factors
Affecting Soil Permeability
learly all of the work that has been
done
on the factors
which
affect
soil permeability
has
been
done
in
the
laboratory
and
most of the
results obtained are merely
qualitative
in
char
acter. Much work
remains
to
be
done to determine the magnitudes
of the effects that these 'Various factors have on soil
permea
bility in the field.
•
Intrap-ped
air
A review
of
the literature indicates that air
entrapped
in
the pores of
the
soil is one of the ma^or cause s
for
the failure
of permeability neasuretaents made
in
the laboratory. Evidence
is
lacking on the
effect
in
the
field of air
entrapped
in the
soil
but judging froa laboratory
experiments
it must be of a
considerable
magnitude.
Its influence must be particularly
great during the initial wetting of a dry soil by
rain
or by
irrigation water. As the air is diss olved
in
the percolating
water, its effect on
the
permeability is decreased until after
a period of
tlrae all
of the
air has been
dissolved
out of
the
soil.
Ohristianacn (14) on the basis
of his
work
on the
effect
of entrapped air, concluded that the
permeability
of
the soil
may be reduced to 1/30 of its
air-free
permeability. The
time
required
to
dissolve
the air
out of
the
soil in
the percolate
varied from 3 to 53 days.
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In
laboratory permeability determinations, it was at first
tbought that the air could b® driten
out
of the soil by wetting
the soil
f r o f f l the
bottom. This idea is now
regarded as
falla-
eious
since
it
really
makes
little difference
whether
the
soil
is wett ed from the bottoa or the top. The qualitative reason
for the effect of
the entrapped
air reraains
the
same. According
to
Wyckoff
and
Botset (72)
an explanation of this phenomena
was
given by Jamia for the flow of fluids in constricted capillary
tubes that
contained
gas bubbles. The
presence of
a constric
tion or
an
abrupt change
in diameter
of
the
capillary
acts as
an
obstruction to the
gas
bubble and it will
not flow
through
the
non-uniform
section unless a
certain critical
force is
exerted on it. A bubble advancing into the constricted portion
of
the
tube
must
suffer
distortion which Involves an
increase
in the surface energy at the Interface between the gas and the
liquid at the small radius end of the bubble. This makes the
surface
tension
forces
unequal
with
the net
str ess
being to
drive the bubble back and out of
the
constriction. The appli
cation of a sl ight exte rnal pressure will
only
serve
to
drive
the bubble back into the constriction
where
it will remain
stationary
in equilibriuM
with the
exte rnall y applied
force.
If
this qualitative explanation is valid
then
it does i o t make
any difference
?jhether
the water is
introduced
from
the
top or
from the bottom
as
has been advocated by some investigators.
Since air is soluble in
water and will in
time
be dis
solved in the water percolating through
the
soil, a novel
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-17-
method of eliminating the air from
the
soil was suggested
by
ChTistismsen, Fireman,
and
Allison
(16),
who first displaced
the soil air with carbon dioxide. Carbon dioxide is readily
soluble in
water and when
water is
added
to
the soil
the
car
bon dioxide
goes into solution
and
an
air-free s oil
results.
Wetting the
soil
under
a mcuuffi
is
another technique used
to
eliminate the errors
due
to entrapped air (64).
2.
Microorganisms
Recent
investigation
on
the influence of
microorganisms
on
soil structure and
soil
permeability
indicate that they may
be much more important in
their effect
on soil permeability than
heretofore realized.
Although ffork by early investigators
(69)
indicated that
Microbes
and
their
decomposition products may
influence
soil
perraeability, Allison (l) in
1947 was
the first
to
show con
clusively
the
magnitude
of this
effect. His results show
that
under
conditions of long submergence the microbial bodies and
the
g x j u a s
and
slimes produced in the decomposition of organic
matter
may plug up the
pores
of the soil so that the
permea
bility
is
markedly reduced.
The generalized
perraeability
curve obtained in the laboratory under long submergence is
shown in
fig.
3.
Allison
(l,
p.
440,
441)
gives
the following
explanation
of
this curve.
Phase
1. After initiating
field or laboratory
tests, the permeability decreases to a minimum.
On
highly
permeable
soils
this
initial decrease
is small,
or
nonexistent,
but for
relatively
impermeable soils, it may
be appreciable and
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-18-
F I G .
2
C H A N G E S I N P E R M E A B I L I T Y O F S O I L S D U R I N G L O N G S U B M E R G E N C K -^ H iSOil
PCRMEABtLITY
CW/HR.
STERILe
SOIL
aWATER
STERILE SOIL-REINOCULATEO
CONTROL
70
0
0
0
TIME DAYS
30
0
FIG 3 P E R M E A B I L I T Y - T I M E
C U R V E S
F O R
H A N F O R D
L O A M
U N D E R P R O L O N G E D
S
UBMERGENCE—
AXLISOH
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-19-»
OQatinme for
10
to
20 days before the second
phase of Increase 1®
apparent.
The
decrease
in
permeability
it probably
due
to structural
changes resulting in part from swelling and
dispersion
©f the dry
soil
upon
wett ing and
in
part
to dispersion
resulting
fro»
a de
crease
in
ele ctrolyte content of
the
soil
solution
as any
salts
present
are
removed
in
the percola te.
Phase
2. When
soils
are wetted from the
surface dowiirard,
considerable
air Is
en
trapped in the pores
(l, 10).
As the
air
is dissolved and
removed
in the percolating
water,
the
permeability gradually increases»
attaining
a o a x i i B U f f l ên
al l or nearly al l
of
the entrapped
air is removed, the mini
mum
peraeabllity
appears to be the
resultant
of two
opposing
phenomena,
that
is,
the
forces described for Phase 1 tending to re
duce permeability from the beginning and the
forces
of
air
re»oved
tending to increase
permeability.
Phase
3.
After
the maximim
is
reached,
the
perffleablllty
decreases
with
time,
rather
rapidly at
first
then
more slowly until
after
8
to
4 weeks the
rate
is usually
a
small por
tion
of
its original
value. Frequently it
has
been observed
in
laboratory tests that
the maxiiMUBi permeability
is
reached before
the
last
of
the
entrapped
air
is
removed.
The gradual sealing of
the
soil during
the
third phase
is
due
(as Allison has proven) to biological clogging of the
soil
pores
with microbial cells and
their
synthesized products,
slimes, or
polysaccharides.
Fig.
S shows the results
that
Allison obtained
by using
a
soli
sterilissed
with ethylene oxide gas
as
contrasted to an
unsterilized
soil a nd a sterile
soll-relnoculated. The ster
ilised soils
reach
a constant high
permeability
value whereas
the unsterilized soil and the
sterile
soll-relnoculated
have
decreasing permeability with
time
due to the microbial action
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—20
mnder
long ambaergence.
3.
Salts
All
soils
contain
oolloidal Material
and
the degree
of
dispersion of the oolloidal material has
an
effect
on
the soil
permeability.
This effect is particularly ia5)ortant
in
the
structureless
soils of the fleet (33,
S4)
and of
considerably
leas importance in well-g^gregated
prairie soils of
the Mid
feet.
Harris
(35) in a series
of
classi c experiments on the
perraeability of alkali soils fomd that
the
presence
of
sodium
on the base exchaage
co^lex
caused a decrease in the soil
permeability. The decrease was attributed to
an
increase in
the dispersion of the
colloidal
particles due to the presence
of
sodium in the
base
exchange complex.
In
the reclamation
of
alkali lands
it
has been observed
that
there is an initial
decrease
in
the soil
perraeability
when
the excess
salts
are
washed
out of the
soil.
The
presence
of
excess salts represses the dispersion of the colloids. When
these
salts are washed out the soil is deflocculated
and
the
permeability decreases. In
order to
flocculate the soil again
it ia necessary to replace the sodium
in
the base exchange
complex
with c a l c i x i f f l ?/hieh reflocculates the soil.
4. Temperature
Poiseuille (53) studied
the
influence of temperature on
Tiscosity of wate r and determined the relationship between them.
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-31̂
Hag®n
(1869) irerifiad Poiseuille^s
relationship
and found a 3^
increase in peraeaMlity for every increase in temperature by
one
degree.
Gustafsson
(31)
pointed out
that as long
as Darcy*s law
holds
(laminar
flow) there
is a
linear relationship
between
teaperature and perraeatoility. In the region where Barcy*s law
is Talid only the forces of friation oppose the movement of the
water and these frictional forces are directly proportional to
the viscosity of the wate r.
As an example of the magnitude of the effect of temperature,
in
the spring of the year with water
at
1® C as compared to sum
mer
at
23® G the permeability ratios are 100:163 due to temper
ature.
However Duley
and Domingo
(19)
in
field tests did not
find
any practical
signifioaace in
the effect of
temperature
variations on soil pera®atoility,
F.
Solution of Flow
Probleais
1.
Analytical methods
a. Dupult-yorohheimer theory
Although
the assuaptions
of
the
Dupuit -Forchhei mer t heory
of
gravity-flow
systems
have
been
shown
by Muskat
(51, p. 359)
and others
(fO)
to be
so questionable as
to
make
the
whole
theory
untrustworthy, its widespread use even today makes it necessary
to
consider
it
in
some
detail. (It
should
be
pointed
out that
although the t heory is based on erroneous
ass\«nptions
the results
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22
that
are obtaiaed are
often
surprisingly close to those given
empirically
or
by exact calculation.)
Dupuit
assumed
that
for small inclinations
of
the free
surface
of
a gravity-flow system the streamlines can be taken
as
horizontal, and are to toe associated with
velocities
which
are proportional to the slope of the free surface, but arc in
dependent of
the depth. la
other
words,
all the flow is in a
horizontal direction and the
rate of
flow depends
on
the
slope
of the water table, fhis i® of course contrary to the flow
patterns obtained
in
sand-tank experiments (34)
and
electrical
analogues
(10) and analytical
solutions
(44), which
have
shown
the true, circuituous paths taken by wate r particles. The
theory
thus assuaes that a system will
have
no gravity-flow
characteristics
which is
entirely
contradictory to the impli
cations of Barcy's
law
as
pointed out by Muskat (51).
lumeroua investigators
(2,
17,
46,
47)
have applied
the
Dupuit-Forchheimer theory to the problem of
land
drainage and
although the aathematical devices used to get their results
have differed, the equations derived
are
a ll
very similar.
Russell
(59)
has discussed the literature
on
the subject be
fore 1934 and the following example will largely follow his
text.
Certain assuiBptions
are
aiade:
(l)
the
soil
is
homog
eneous; (2)
rain
water
percolates uniformly
through
the
soil
till
it
reaches the water table which starts rising;
(3)
when
the
ground
water reaches above the drains, it
will
start to
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~.S.3-
flow
lato
them, the
rate of movement being greates t
in
their
iramediat#
neighborhood
and
slowest
halfway between
the
drains;
(4)
the
me&n
horizontal
oomponent,
v,
of
the
rate
of
flow
through any cross section PQ is
proportional to
the slope,
of
the groimd-water
aurfaee at
P,
and, {5) no
\mter move-
QX
f f l e a t oijcurs through
the
subsoil below
the
drain level AB.
The
derivation follows: (See
fig.
4)
*
fed.y
dx
C i
a
kŷ
dx
Sinee the
ground
water surface reaains stationary, Q
is
equal
to
the
amount
of
water
percolating
downwards
from the
soil sur
face In unit time between P
and 0, therefore
Q
a t q(̂
- x)
where
q
is the a f f l o u a t
of
water
percolating in unit time per
unit area of
soil
surface, therefore
and on integration
ic.y^
a EX -
i
This
ie the equation of
an
ellipse
with
center
at
D and semi-
I ' l
1
axis
1
and
fhus
the s u m f f i i t
of
the
ground-water
surface
reaches a maximm height h; where h
«
Hence
if the
drains
are laid at a depth
the
ground water will not
rise
above a
depth
h* below
the
surface where
h* s d-h.
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G R O U N D S U R F A C E
Free Water Surface
(Phreatic
Surface)
D R A I N
T U B E
D R A I N
TUBE
E
Fig.
4. Dupuit-Forchheimer Theory of Soil Drainage
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The
equation
may b@ re-writtern
d -
-
=
I
K
is
determinable
and
bene# if
q (the
maxin^ra rate of
influx
of
water whieM the system will be required to deal
with)
is
known,
the depth and spacing
can
be chosen
in
such a way
that
the ground water will
neirer
rise nearer
to
the surface than
soiae
specified
distance h,
®hieh must
be sufficiently great
to present damage
from
water-logging.
b.
Kirtehaa-Gardner
approach^
ly assuming a steady state condition with
the potential
function
(or it s aormal derimtive) known over the boundaries
of the region considered, it is
possible
to get solutions
of
liaplaee*8
equation that will satisfy the known bomdary con
ditions. These solutions
can be
used (after considerable
mathematical manipulation) to determine
the flow
into drain
tubes embedded in the soil, Slichter (63) first pointed out
the possibilities of this approach and Gardner et
al
(39) made
application
of
it
to the problem of artesian flow. Recently
Kirkham
(43) has
solved
the
problem
of
flow into a series of
drain tubes embedded in a hotaogeneous soil. In addition he
has
solved the problem of flow into drain tubes embedded in a
two-layered
soil
(4(4),
each
layer having a
different
permea
bility. These solutions were obtained
using
the method
of
images (See
Muskat
51,
p. 175)
and the
results
were
expressed
in
conjugate fmctions. The real and imaginary parts were
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26
separated to give a potential function a j i d
a
stream function.
The normal derimtlre of the potential was obtained at the soil
surface and this aortaal
derlirative
was then integrated over the
surface of
the
soil.
Multiplication by the
soil
permeability
gave the quantity of wate r flowing across the surface of the
soil and therefor© the quantity of water flowing
into
the drain
tubes.
In this analysis the assumption was made that the surface
of the soil was everywhere at the saae potential
(ie.
ponded
water). The falling
water
table was not taken into
accoiint
in
lirkha®*s. analys is,
2. Qraohical
method of Daohltr.. Gasagrande. and Forchheliaer
Muskat
(51)
la
a
discussion
of Daohler^s work, described
the
application of
the graphical
method to
seepage through
dams made of permeable material, fhe Initial problem is the
location of the surface of seepage. The Inflow face, main body,
and outflow face of the dam are treated as separate
flow
sys
tems
by
different
approximations,
and are
then synthesized
by
the
requirements
that
the
fluxes through
each
shoxild
be
equal,
and that the fluid heads should be continuous in passing from
on®
part
to the
other. 4fter
the
surface of seepage
has been
located, the
equipotential
lines,
each one
representing
a
con-
stiunt fraction of the total loss in head h, are drawn. Streanh-
linea are chosen to be orthogonal to
the
eqiAipotential so
that
the saae fraction of the total seepage passes between any
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-27-
pair
of neiglibo3rlag flow lines.
The
resulting net
will
consist
of a series of
squares. If one
aueoeeds in
plotting two
s e t s
of
curTea so that
they intersect
at right angles,
forraing
squares
and
fulfilling
tbe boundary
condition, then
one
has
obtained a
graphical solution
of
the problem. Oaaagrande
(9)
applied the method
to
soil® which are anisotropic with regard
to permeability. He showed that a ll dimensions in the direction
k max are reduced by the factor A/KsIb or all dimensions in the
V k
max j—
—
direction of t mlm. are increased by the factor
Vk̂ n*
probleffl is solved for the
case
of a soil
with
uniform permea
bility and then the above conditions are applied.
The average
permeability will be
¥* k
»in
k max
and
the
flow
will b®
q « t
A
where
is
the
directional
derivative
of the
potential.
The answer obtained by use of the graphical method is
only
approximate but
is
of the correct order
of
magnitude
and
use has been made
of
the
method
in the
design of
earth dams.
3. fhe
hodograah
A
hodograph
is
a representation
of a dynamical
system
In
which the
coordinates
are
the
vel ocity components
of
the
particles of
the
system. The
method
of
treatment is
difficult.
A
description
by Muskat (51) will be
followed
here.
Although
the method was developed earlier by
Helmholtz and
Kirchoff,
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28
Haael (33) first made considerable application of it to t^o-
dimensional
seepage
systeffls, fhe systems
included
simulta-
neoualy
ii^ermeatole boundaries, constant-potential surfaces,
and surfaces of seepage, fhe liodograph of a
flow line is
the
cunre which
one
obtains
when
plotting
from
one
origin
velocity
vectors for all the points of
the
flow line,
^e
straight line
Gonneeting the origin with on®
point
on
the hodograph represents
the
fflagnitude and
direction of
the
velocity
for
the correspond
ing
point
in
the
flow line.
Since the
velocity
along the
free
water
surface is
propor
tional to the Bine
of
the
slope,
the hodograph
for the line of
seepage
is a circle with diameter
equal
to
the
coefficient
of
permeability.
The hodograph for
a straight boundary is a
straight
line.
Once the boundaries of the system are fixed (in the
hodograph plane) the
methods of
conjugate-function
theory
can
be applied
to
the final
solution
of the problem, although
the
transformations
of
the circular segments representing
the free
surfaces
involve
the theory of
modular
elliptic functions
(See
Musfcat
51, p.
301).
4. Mesi^rane
aaalomie
la
a
study of the
uplift
pressures
on
large
dams,
Brahtz
(8)
developed
a
ajembrane analogue to
obtain solutions
for two-
diaiensional probleffls* Bie analogue
takes
advantage of the fact
that
the differential
equation
for the
steady
st a t e
potentials
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«29-,
for the percolation
witMn
an earth or concrete
mass
has the
same
form as
the differential eqmatioa for small
normal defleo-
tiona
of
a «nifor»ly
stretched
rubber mefflbrane (Laplace's
equa-
tioa). The relative ordinate s a t
a l l
points along
the bound
aries of the membrane are
made
proportional to the boundary
pressures at
corresponding
points in the structure. The or
dinates at a ll
interior
points
will then be proportional to
the pressures at corresponding interior points in the proto-
type.
The analogue is set
up to represent
the
field conditions
and the ordinate s of the rubber membrane are meas ured by
meajas
of a micrcmeter device.
The
a®sufflptions B»de in the use of
the meiabrane analogue
are
(1)
the materials of the
d&in
and the foundation are
honKJg-
eneoms (2) the merabrane
i® of
infinite extent
in
a ll directions
(3) the
membrane is
only slightly displaced*
llestrlcal analogue
The electrical
method
of flow analysis
in
seepage problems
was first proposed by Pavlovsky in 1932
[^Bee
Low, Dams, Natl ,
les.
Com®,
1938
Wash.
D.O.,
for
a
discussion
of
the electrical
method] and is based on the relationship between Ohm's law and
Darcy*e
law.
O h f f i * s
law, which
expresses the fundamental rela
tion
for the fl ow of
an electric
current, is expres se d by the
equation
i a
-
o- (6)
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where i
s
curreat
per imit area
speoiflc oonductivlty
voltage gradient in the direetion s.
The
minus
siga
indicates that the potential decreases
as
the current progresses
n
the positive
direction. Darcy*s
law for the
flow
through
porous
media is
Q
• |4. (7)
OS
where
Q
« quantity of water flowing per unit area
k « permeability (or conductivity)
hydraulic
gradient
in direction s
Equation
(6)
is
identical with equation (7). Since the
princi
ples
of flow
are similar, with the saaie
conditions
as
regards
pressure and path
of
flow, the
flow itself
will be
similar.
The electrical analogue
can be used to
trace both the
flow
net and the equipotential
net
and the resulting figures
can be
used
to
coapmte
the quantity of
flow
throiigh
the
sec
tion
investigated*
Ohilds {10» 11, 12, 13)
has
made the most intensive
appli
cation of the
electrical
analogue method
to
the study of land
drainage.
He soaked sheets of filter paper in colloidal
graph-
it© a nd
reproduced a section
of
the field
case.
A copper
foil
T s a ©
used
to
represent the
drain tube.
The vertical
flow
in the
soil
above the water table was represented by current input
between a
series of strips conducting
material
insulated from
each other.
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-31-.
6.. Muwerlcal
methods
Iimcrical
methods
of solving two-dimeasional partial
differential equations
involve
the replacement of the con-
tinmum of points in a
region
considered, by a discrete set of
points, and the replacement of
the
differential equation
by
a
finite difference equation. Llebmaan (48) was
the first
to
show
how to
replace Laplace*s equation by
a
finite difference
approximation and
obtain a
solution by an
iterative
procedure.
In
the process
developed by
Liebaaan, a square
net
of points
is laid
over
the region and approximate values (best
guesses)
of
the function are assigned to interior points while known
values
of
the function are placed on the boundary points. The
net
is then repeatedly traversed, replacing the value
at
each
interior
point
by the
mean of
the
values at
the
four neighboring
points,
using the new values in
the
improvement of
the
succeeding
points.
After
a
number of traverses,
the
function
a t each point
will converge to a
solution
of the finite difference
equation.
The accuracy of the answer obtained and the rate of convergence
-will
both
depe nd on the size of the net spacing.
The difference
between the solution of
the
approximating
difference eqpiation and the differential equation representing
the true
solution
has
been
investigated
by
Richardson (58),
showed that on a net of interval h the difference is of the form
A
(X,y)h^+B(x,y)h^4-C(x,y) h®+ —
Since
only even powers
of h enter
here, the
difference
solution
approaches the differential solution rapidly
a s h
approaches
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33-
2«ro,
As
pointed
out
toy Shortl«y
et
al (62), if h is suffi-
0i®Btly siaall the error is
proportional to
and
by
making
two solmtions with different h, one can
estimate
the differ-
#a©e of @a(^ from the solution of
the
continuous problem,
Shortley,
Isller,
and Fried (62) have
studied
the rate
of convergence of the Lietomann procedure by investigating the
rate of
convergence
of an arbitrary *error" function as the
s a f f l e iaprovement
formla
is used repeatedly. The "error*
function has zero botindary values
and
converges to zero every
where in the
region,
the rates of convergence of
the "error*
function
and the true
function are the
same.
As a
result
of
their investigations they conclude that
the
rapidity of
con
vergence
varies inverse ly
as
the number of points in the square
region under consideration, for example, the error at any point
in a square region with
81
interior points
is
reduced to about
nine-tenths
of
itself
by each
traverse after it has been
im
proved a few times. At this rate, it would take about 23
traverse® to
reduce
the
error to
one-tenth
of it s
initial
value.
For
a
net
of
389 interior
points, about 75 traverses
would be necessary.
In an effort
to speed
up the rate of convergence,
various
procedures have been devise d «hich trea t whole groups
of
points.
This so
called
block procedure
has
been applied by Shortley
(62), Southwell (65), and others with success.
Southwell (65) developed the relaxation* method which is
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• 33 »
superior to the
Itiebaiaaa
proeedure in the length of tirae
re
quired to solire th©
protolem. fhe
relaxation method was devel
oped
froBi
a
consideration
of statics
problems
and Southwell
generally
speaks in termt of a tension net as an approximation
to
a soap
film
or membrane. A
simple explanation of
the
relax
ation method has been given by Imroons (21).
In the
relaxation method, instead
of
dealing
with
the
values of
the wanted
ftinetion, ( j >
, at
the interior points the
residuals are compute d and recorded. Referring to fig. 5 the
residual
R is
coE^uted
by
the foranila (the prime indicates
that
the value
is
an approximation)
R « 4 > ' ( i > ^ - H
+
i > ^ < i > ^
fhe
R thus coi^uted can be thought of as an interior sink which
a i t t S t be reaoved. If
0'
is altered at any one point, there will
be a change
in
the
residuals at
each of the
four
points
sur
rounding
d ) '
.
pecifically,
if
is alte red
by
-4
units
each
of
the
residuals at th® f our
surrounding points will increase
by one unit,
lach
change
of
a < P ' at
an
interior
point
will
cause a redistribution
of
the residuals
according
to
the
"relaxation" pattern of
fig. 6. Hie calculator adjusts 4'
and the
H*s
until the residuals are sufficiently small. The
problem
is
then considered solved.
An
interesting
application of
the relaxation method has
been
made by
8/16/2019 A Piezometer Method of Measuring Soil Permeability and Applicatio
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4 ) ,
^4
(I)o
( | ) 2 .
* ^ 3
fiit
S.
fif# i# fnflwtii
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•3 ~'
nscted toy the
Gauehy-Rieffianm
eqmatioas.
5
0
^
a
tp .
^
^ y
Sx'
)^ '
Gilles developed suitable equation®
so
that the two wanted
func
tions, f
&mi < p
can
b® deterffiined
siaultaneoualy. However in
his words, *The process is
both
laborious and tedious*.
Moskovitz
(50) has
presented
a process which yields pre
cisely
the
convergent
values of the
function
obtained by
in
finitely Biany traverses of the region, fhe
Liebmaim
formula
is used for several traverses; then, succeeding values of
the
improved function are caloulsted by aeaas of tables
included
in
Mo8kovitE*s paper.
Only
regions with
rectangular boundaries
can be
treated
by this aethod.
Shaw
and Southwell (61) have applied the relaxation method
to probleffis of percolation
under
a da® and
have
treated the case
of flow thro^u^ layered porous material having different permea
bilities in each
layer.
Fox (25)
has
shows
how values
of
the function may
be com
puted at
points
close to an
irregular
boundary.
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36
III.
fHE
PROBLEM
The problem
can
be
divided Into
three rel ated perta,
(l) the dev#l©pffi©nt of a field procedure of measuring soil
peraeability beneath a
water
table, (2) the
use
of the three-
dimeasional
electrical
analogue
for
the determination of cer
tain
constants
in
the
perffleability equation and the use
of
the
el ectrical analogue in the study of soil factors affecting
flow,
(3) the application of peraeability data to a drainage
problem solved by numerical aethoda,
A. PieEometer Method of Measuring
Soil
Permeability
1* pmcedur#
The
field procedure
as
finally developed
is a s
follows:
The surface sod is removed from the soil and a hole
is
augered
out
to a depth of about 6
inches
below the
surface
of the soil.
The auger used is one
of
1/16 inch smaller diameter than the
inside
of
the
piezo®et«r.
A piezometer (which
is an
unperfo-
rated
pipe)
is then driven about
5
inches
into
the auger«d-out
hole. ,(One inch thia-walled electrical conduit
has proven
satisfactory
for
use
as
a
piezsmeter.) The
auger
is inserted
inside of the piezometer and a cavity is augered
out
for another
six
inches
below
the end of the piezometer which is then drivea
with light taps
of the aaul
(fig. 8) into the soil for another
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-37-
SOD REMOVED
IEZOMETER
^SOIL
SURFACE
\ i n 1 I
/
I I
I
I I I I
WATER
TABLE
- 2 R
7
I
/
I ^ C A V I T Y
s
2r
^
/
FLOW
LINE
IMPERVIOUS
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1
I
I
LAYFR
/ i / i
I I I I I I I I I I I I 1 1
7. Pl@zQ«©t«? Met&od of Mea8iuf«m«at of
Permeatolllty.
8. lastailing th© Piezometer.
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—38*
5 inoliea, Tkis procedure of
successive augerings
I s rep«ated
until t l i e piezoaeter is at
the
desired depth
below
the
surface
of the soil.
It
should
be
emphasized that the
piezometer
is
always forced
into
a
cavity
with diameter slightly smaller
than that of the inside diameter of the piezometer. It is
never forced into natural soil
without augering.
Ihen
the
piezometer is at the desi red depth a cavity of
any convenient length is a ugered out beneath the piezometer.
Water will flow into this cavity during
the permeability
t est
and it is essential to auger it out with care.
fhen the
piezometer
ha®
been placed at the proper depth,
a hose from a
pump
is lowered to the bottom of the piezometer
and the cavity is flushed, t© remove puddling effects, by
puffiping out the
in-seeping water
(fig.
9). In more
permeable
soils the
cavity is
quickly
flushed
out
while
in tight clay
soils
the
water may seep
in
so
sl owly that
it is
necessary
to
apply suction to the pipe to speed
up
the process (fig. 10).
Permeability
measureaients
are
then aade by
pumping
the
water
out
of
the piezometer
and
measuring the
rate of
rise
of
the water in the piegoaeter. An electrical
probe
which works
on the
principle
that
an electric circuit is completed
when
the end of the
probe
touches
a water
surface, may be
used
to
measure the water elevation
in
the
piezometer.
fhe level of
the water
table must also be known for the
calculation
of
the soil
permeability. In
highly permeable
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-39-
10
Applylag
Suetion
Upper Stopper
la
Piezometer.
to
the
Piezometer,
for
a 2-incto
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40
soils It takes only a few minutes for the water table to
establis h itsel f. In tight olay s oils it may take
hours
ox
even
days
for
the
water
table to
reach
an
equilibrium
state.
When the
laeasurement
is
coiapleted,
the piezometer is
removed
from
the
soil by means
of a soil tube jack.
2 , Field t est s
Preliminary tests on prairie soils under continuous pas
ture showed that it was
essential
to
remove the surface
sod
before installing the piezometer. Forcing
the
piezometer
through the sod caused a ball of roots and soil to
form upon
the end of the piezometer. This plug compressed the soil
around
the
end of
the pipe and reduced the permeability.
Two types of
ai;^ers were tried in field tests;
one
a
regular carpenter's bit with the sharp
edges
ground
off, and
the other a double-twist-type soil ai^er. In
heavy
soils
there was
less tendency
for
the saturated soil to
slip
off
the
carpenter's
bit
than off the
soil auger. Other than
that
no particular advantage
was
noted for e ither auger. It was
found
advisable
to
use
small-diameter pipe
(3/8
in.) for
the
handles of the auger so that it was impossible for the operator
to take
large
bites
of
soil.
Soil puddling
and
compression
were minimized by taking
small
auger bite s. The
auger
shaft
was conveniently marked with brass
tips
so the operator could
tell
the
depth
of the
hole.
Any si ze of pipe could probably be used for a piezometer
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-41-
in these tests. In the first field trials 3/4" iron water
pipes were used
and
were
satisfactory
for
the iBeasurement, but
their
weight made
them
difficult
to transport
in
the
field.
In
addition, water
pipe
corrodes
very
easily. The pipe that
proved
most
satisfactory
was thin-walled
electrical
conduit,
which is
light-weight, strong, and
resists
corrosion. Three diameters
of
conduit were tried, 1.0, 1.5, 2.0 inches and all of them
worked satisfactorily. Conduit is available oommercially in
10-foot lengths.
These
lengths
were cut
in half
and one
end
,
was
beveled
to
provide a
sharp
cutting
edge. The
pipe
was
marked at 1 foot intervals
with
paint. This
was
not
very
satisfactory since the paint wore off after
a
lit t le usage.
A more satisfactory method of marking
the pipes
would
be to
cut a shallow groove around the circumference
of
the pipe
with
a
pipe
cutter,
A driving head made of steel was placed on the piezom
eter
while it was
being
driven into the soil to protect the
piezometer from
the
battering action of the
maul
(See fig.
8).
The puap used
to puap
the water out of
the
piezometer
was a small pitcher
coiimonly
foxmd on farms
(See fig.
9).
A pipe
connection
extended
above
the
level
of the
pumping
cylinder
so
that the ptamp would not lose its
prime
between
operations. In field
tests
a suction of about
0.75
atmos
phere was developed
by
the pump. It was found necessary
to
soak
the leathers
on the pumping
piston
in water before using
the pump. No other pumps
were
tried and no
particular advan
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tage iB cla imed f or the pwmp
here
deseribed although it should
be
pointed
out that t h i e
pû
is of
rugged construction
and no
difficulties were encountered in its use in the field.
Plastic garden
hoae
with an Inside diameter of 17/32 inch^
and outside diameter of 15/16 inch worked
very
satisfactorily,
fhe inside diamete r was
large
enoi^ to pass sand-and small
gravel and the wall was sufficiently rigid to stand up under
the suction.
Rubber
tubing was not satisfactory because of its
small inner diameter and
because of
the
flexibility
of the walls
fwo
types of electric probes were tried.
The
first con
sisted of a wooden rod with
an
embedded wire. One
end
of the
wire protruded from an end of the, rod. The other
end
of the
wire was connected in series with a milliamiaeter, a 33-volt
hearing-aid battery* a limiting resistor and a brass collar
that
fit
ow@T
the end of the piezometer. Ihen the wire pro
truding from
the end
of
the wooden rod touched
the
water
sur
face in the
piezometer
the
circuit
was completed causing^ the
milliammeter to deflect. The wooden rod was graduated in
inches
and a
set screw in the brass collar enabled the
oper
ator
to
fasten the rod at any
elevation.
leadings
were faade
in
the
following
ma^er; the rod
was
set at
a o r a e
predetermined height
and
the
operator waited un
til
the
rising water in
the
piezometer reached the rod.
A
stop
watch
was
thegi started
and the
rod
teoved up on® inch
(or any desired distance). lh.en the water level reached the
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new elefatioa
as
Indicated by
the deflection
of
the
milliaffi-
meter,
the first s top
wateh
was st opped and a second stop
watch st arte d, fhe reading on the first s top watch recorded
and it wes reset
to
zero so that it could be used again to take
the third
reading.
In this way it was possible to get a whole
series
of
aecurate readings
using
two stop watches.
The collar
attachment that
fit
over
the end of
the
pipe
also
held a small
horizontal
square of plywood that served as
a
platform
for
the ffiilliaaaaeter,
the
battery,
and
a notebook.
The rod-type
of probe was not
very satisfactory for two
reasons, (l)
it
was awkward
to
carry in a oar and in the field,
(3)
it
took an
appreciable
length of time
to
reset
at
a new
elevation.
Because
of these liaitations a new
electric
probe
waa designed following,
somewhat,
the
design
of
CSiristiansen
(15). A fishing reel (Oreno So. 1165) was faste ned on a
square
of
plywood
(See
fig.
11)
and
a
graduated length
of
radio
test
lead
wire
was wound
on
the reel. A weight consisting
of
an insulated brass slee ve
fit over
the e nd
of the
wire that
dropped
down inside
of the piezometer
and
the
other
end
of
the
wire
was
hooked onto the reel. There was sufficient friction
in
the
catchment ae chanism of the reel to hold the
wire
at any
desired elevation. The reel-type probe proved to be more con
venient to operate in the fie ld and
was
ouch more compact than
the rod-
type probe.
It could be operated with